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Question
The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at ______.
Options
(0.6, 1.6) only
(3, 0) only
(0.6, 1.6) and (3, 0) only
at every point of the line-segment joining the points (0.6, 1.6) and (3, 0)
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Solution
The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at at every point of the line-segment joining the points (0.6, 1.6) and (3, 0).
Explanation:
The minimum value of the objective function occurs at two adjacent corner points (0.6, 1.6) and (3, 0) and there is no point in the half plane 4𝑥 + 6𝑦 < 12 in common with the feasible region. So, the minimum value occurs at every point of the line-segment joining the two points.
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